Multiple Choice
Solve the system of equations using Cramer's Rule.
18. Systems of Equations and Matrices
Determinants and Cramer's Rule
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Evaluate the determinant of the matrix.
A
165
B
9
C
63
D
25
Verified step by step guidance1
To find the determinant of a 3x3 matrix, use the formula: det(A) = a(ei − fh) − b(di − fg) + c(dh − eg), where the matrix is [[a, b, c], [d, e, f], [g, h, i]].
Identify the elements of the matrix: a = 4, b = 1, c = 2, d = -5, e = 2, f = -3, g = 1, h = -4, i = 6.
Calculate the first term: a(ei − fh) = 4(2*6 − (-3)*(-4)).
Calculate the second term: b(di − fg) = 1((-5)*6 − (-3)*1).
Calculate the third term: c(dh − eg) = 2((-5)*(-4) − 2*1).
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